Keywords: water mains, failure prediction, non-parametric, maximum likelihood estimation, probabilistic.

In addition to the physical characteristics, there are a range of environmental and operational factors influencing the mechanism of failure of pipes in water distribution systems [1]. Some of these, are non-stationary random variables. Resulting non-stationarity of pattern of failures over time can not be accurately modelled with specific probability distributions, with time-invariant parameters. This study presents a non-parametric failure prediction technique which is considering the non-stationary nature of failure process. This technique is applied to the failure history of cast iron pipes in the Western suburbs of Melbourne to estimate the expected number of failures for each group of pipes, within a number of time intervals in future. Furthermore, an 80% confidence interval is determined for the estimations. The presented method implicitly considers the gradual variations of the factors influencing the deterioration process. In other words, the outputs of the prediction method are automatically updated with time.

At the first step, failure history is divided into some intervals considering the frequency of failures. The ensemble of probabilities of occurrence of k failures during each time interval are called the Likelihood of Number of Failures (LNF). For a homogeneous group of pipes, histogram technique is used to calculate the LNF values in each period (a number of time intervals). The binary proposition "k failures occur during the n-th time interval" is denoted by NOF_k(n) where NOF stands for the "Number of Failures" and n is the interval number. The times elapsed between consecutive NOF_k events are the corresponding inter-failure-times. For each k, set of inter-failure-times are empirically calculated using the failure history.

In this technique, the problem of prediction of LNF values is turned into prediction of inter-failure-times. To predict the inter-failure-times, Finite Impulse Response (FIR) filters are applied. Predicted inter-failure-times are used to estimate the LNF values in the next time interval. The probabilistic values for a given time in future are estimated based on convolution theorem. From these, expected number of failures in a time in future, are estimated, along with a confidence interval for the estimation.

The method presented implicitly considers the gradual variations of the factors influencing the deterioration process. In other words, the outputs of the prediction method are automatically updated with time. This is because every time interval corresponds with a NOF value and adds a new time interval µ_k to the record.

An inverse relationship between the accuracy of predictions made for inter-failure-times and the corresponding LNF values is realized and demonstrated. This shows the high tolerance of the method to the possible inaccuracies in selected inter-failure-time predictions that is a point of strength for the technique.

It is also illustrated that, the accuracy of prediction decreases as the range of prediction widens. A step by step algorithm for applying this technique on a pipe failure history is presented. An illustrative and quantitative comparison of the accuracy of estimations performed by proposed technique and simple averaging method exhibits the satisfactory performance of developed technique.

1

Y. Kleiner and B. Rajani, "Forecasting variations and trends in water-main breaks", ASCE Journal of infrastructure systems, 8(44), 122-131, 2002. doi:10.1061/(ASCE)1076-0342(2002)8:4(122)

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